practice1(2) - Practice Exam 1 MAP 4305 1 Does xy(x 2)y y =...

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Practice Exam 1: MAP 4305 * 1. Does xy ′′ + ( x + 2) y - y = 0 , x > 0 , have a solution which is bounded near zero? Notice that to answer this question, you only need to consider the indicial equation. 2. Determine the form of a series expansion about x = 0 of 2 linearly independent solutions to: x 2 y ′′ - xy + (1 - x 2 ) y = 0 , x > 0 . Do not find a recursion formula for the coefficients. 3. Let J ν ( x ) be the Bessel function of the first kind of order ν 0: J ν ( x ) = summationdisplay n =0 ( - 1) n n !Γ(1 + ν + n ) parenleftBig x
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